The Science of Discworld IV

are statistics-blind. They comment on the very apparent decline of violence in the last few centuries as if it were
only
apparent, unsupported by valid observations. Almost none of the comments are from positions that are modern and balanced; nearly all are from arts
or
science viewpoints, but not both.
    Now that the division between mind and matter has been buried, or at least is on its way to the cemetery, how do we think about causality? Well, here is our second example, which splits into three related issues: day and night, the rainbow, and turning a light switch on.
    What causes day and night? The answer is easy and obvious. fn2 It is a question of gravitational forces, working according to the law of gravity, and the Earth turning on its axis so that it presents different faces towards the Sun. The Earth turning, about once per twenty-four hours, is what causes day and night. Easy.
    Now let’s think about a rainbow. Here things are a little more complicated. Jack sent each of his six children in to school to ask the teacher what made a rainbow. In each case the teacher gave what we’ve elsewhere called the lie-to-children response: fn3 ‘A raindrop is like a little prism, and you’ve seen how a prism breaks light up into colours.’ ‘No,’ said Jack’s children, ‘it’s the sharp bits on the prism that break up the light, and there aren’t any sharp bits on raindrops. Anyway, we understand about raindrops refracting light, we want to know why there’s that wonderful great bow in the sky.’ And all the teachers said ‘I don’t know’, variously, and two said, ‘When you find out, please tell me,’ and got great plus points for that.
    The children were wrong about the sharp corner of the prism: it still refracts if you round the corner off. But they were right to focus on the shape of the rainbow, rather than its colours. Until you explain the shape, it’s not clear why the colours, emitted by millions of different drops of rain, don’t smear out.
    What actually happens is quite complicated, though known to Descartes. Sunlight striking each drop gets refracted (and broken up into different colours) and then it bounces (total internal reflection) and passes out back towards the Sun, the different colours being further separated. Some fancy geometry shows that there is a focusing effect, because rays that enter the drop behave differently according to where they hit. Most of the light of a given colour comes out in a concentrated ‘beam’ at an angle of about 67˚ from the direction it went in. This angle depends on the wavelength, that is, the colour, of the light. So, if you’re standing with the Sun behind you,you see the backward-pointing coloured spray of rays from those raindrops that form a 67˚ circle in the sky. Someone standing a metre to your right doesn’t see
your
raindrops, but those corresponding to a
different
circle a metre to the right of yours.
    Many years ago when the world was young, Jack was training to be a rabbi, and he grew up with a reasonably-firm conviction about God, Abraham and the covenant between them (Genesis 9 verse 13). He was delighted by rainbows, and still is. What a nice idea … but quite a complicated way to achieve it. And didn’t light get refracted in exactly that way before the covenant? Now he sees rainbows as grace notes in the physical world, apparently unlikely processes that are delightful, or the evolution of frogs, whose developmental programme has to work in wildly varying temperatures, requiring a longer genome than our own. He doesn’t implicate a god in these things, but he is grateful nevertheless. He does genuinely wonder whether humans are the only creatures that enjoy rainbows, or indeed enjoy at all. Still, rainbows were ‘there’ long before humans came on the scene. Perhaps the crab civilisation (
The Science of Discworld
chapter 31, ‘Great Leap Sideways’) enjoyed them.
    So much for the causality of rainbows: complicated physics, but a delightful outcome.
    Now we come to a really difficult bit of causality; turning a light on. You think this is simple too? Not a bit of it. You go into a room from a lighted hallway, and the switch is there. All kinds of clever neuronal things happen, sensory things and motor things, and the result is that the muscles in your arm lift it so that your finger can work the switch. You press (or turn or whatever) the switch, and the connection is made. Now alternating current can participate in